Mathematical Modeling of Composite and Inhomogeneous Deformable Materials Based on Scanning and Finite Element Method

摘要

The paper presents a method of mathematical modeling of composite and heterogeneous deformable materials used, in particular, in modern aircraft structures, such as MS-21. The technique is based on scanning a deformed body by a computer tomograph, with further mathematical transformation of the information obtained for its use in the finite element method analyzing the stress-strain state of parts made of composite and heterogeneous materials. Traditionally, the mechanical characteristics of a real deformable solid body are given as an average value, for example, common for the material of the part and obtained during the test of standard samples. The main purpose of the presented technique is, along with improving the accuracy of calculations, the determining of the level of defects in the material and the degree of its impact on the performance of the product as a whole. The method for determining the real change in the mechanical characteristics of the material of deformable solid bodies is based on the use, on the one hand, of the pixel characteristics of raster images scanned by a computer tomograph; on the other hand, the averaged data on the mechanical characteristics of the material obtained as a result of full-scale tests of standard samples are used. The result of this approach makes it possible to simulate these inhomogeneities in the construction of a finite element model of real deformable solid bodies. The developed approach can be applied to any physical principles of scanning, such as x-ray, ultrasonic, laser and etc., as well as for all types of materials when the information obtained as a result of scanning is formed in the form of a digital (raster) image.